# Direct, Inverse, and Joint Variation Calculator

## Calculate direct, inverse, and joint variations step by step

The calculator will find the constant of variation and other values for the direct, inverse (indirect), joint, and combined variation problems, with steps shown.

### Solution

**Your input: find the constant of variation $$$k$$$ given $$$z=k \frac{x^{2}}{y}$$$, $$$z=7$$$ when $$$x=5$$$ and $$$y=3$$$ and find $$$y$$$ when $$$z=12$$$ and $$$x=1$$$.**

We have that $$$z=k \frac{x^{2}}{y}$$$.

Plug in the given values to find $$$k$$$: $$$7=k \cdot \frac{5^{2}}{3^{1}}$$$.

Solving this equation, we obtain that $$$k=\frac{21}{25}$$$.

Now find $$$\mathtt{\text{y}}$$$.

Plug in the given values and found $$$k$$$ to find $$$y$$$: $$$12=\frac{21 \frac{1^{2}}{y^{1}}}{25}$$$.

From this equation, we have that $$$y=\frac{7}{100}$$$.

**Answer: the constant of variation is $$$k=\frac{21}{25}$$$, $$$y=\frac{7}{100}$$$.**